Pairs Trading; A Comparison between Student-t and Vine Copulas

The main purpose of the present research was to compare the performance of pairs trading based on the Vine Copula, Student's t Copula, and Distance approaches. This was done for the first time on the Tehran Stock Exchange (TSE). The main advantage of the Copula approach over other common approaches in pairs trading, such as the Distance approach, is that in this approach it is not necessary for the stock return distribution to follow the Gaussian distribution.

In the Distance approach, for each sample stock, a stock with the same price behavior was selected, the undervalued stock was bought and the rest was sold. In the Copula approach, first, similar stocks were selected using the traditional and geometric approach. Then Copula functions were fitted among stocks. In Vine Copula, different families of Copula were fitted and the best Copula was determined based on the Akaike Information Criterion (AIC). Then, the pairs with the most mean-reverting characteristic was selected and transferred to the trading period, in order to execute appropriate trading positions. Finally, the return, Sharp ratio, Value at Risk (VaR), maximum drawdown of the Distance approach strategies, the Student's t Copula and the Vine Copula, were compared. The performance of the pairs trading strategy was tested according to the downtrend and non-downtrend conditions of the stock market.

Both Copula approach strategies produced higher returns and Sharp ratios than the Distance approach and the Tehran Stock Exchange Index (TEDPIX). However, the Distance approach had a lower performance than the TEDPIX. The annual returns of the Vine Copula strategy, Student's t Copula strategy, and Distance approach stood at 194, 171, and 20 percent, respectively. The Sharp ratios of these three strategies were 0.79, 0.70 and -0.04, respectively. Also, the performance of pairs trading strategy in non-downtrend market conditions was better than downtrend market conditions.

As expected, due to the many advantages of the Copula approach over the Distance approach, both strategies based on the Copula approach produced higher returns and sharper ratio than the Distance approach. Also, due to the greater flexibility of the Vine Copula in modeling the dependence structure, this Copula could produce a higher return and Sharp ratio than the Student's t Copula.